I do not think you are doing anything wrong. Emoji's are special ASCII 3 byte characters, part of the extended character sets also used by non-English alphabets. It does require that the software handle 3 byte characters, not all field types and character sets do. In Memento, it appears that regular text fields are capable of handling the extended character set and emojis, but the "Rich Text" type fields do not.
The developer of Memento does not always read this forum, so you might want to report this directly to him. Go to the Memento Database web site (
mementodatabase.com), click on "Contact", then click on "Submit Support Request" and fill out the form.